As the positioning methods, the hyperbolic navigation methods represented by the methods such as the Loran C navigation method or the omega navigation method were popularly used in ships or airplanes. However, the GPS positioning method is becoming popular and wide-spread because of its very high positioning accuracy. Positioning by the GPS is a technique in which radio waves output from a plurality of GPS satellites are received by a GPS receiver to measure the distance between the respective GPS satellite and the GPS receiver and to calculate the position of the GPS receiver (user). This technique is the core technique for satellite navigation methods for not only ships or airplanes but also automobiles.
However, in this positioning method there is a problem that the radio waves get delayed in the troposphere and the ionized layer. Further, there is an intentional degradation called SA (Selective Availability) generated by the Department of Defense of the U.S.A. in order to intentionally degrade the accuracy in view of the national defense strategies. Because of these problems, in a single positioning method which performs positioning utilizing only one GPS positioning apparatus, a positioning accuracy is about 100 m. At this 100-m-order positioning accuracy, in particular, some problems are posed when a ship enters a harbor or when the GPS is used as a car navigation system in urban areas.
In recent years, a relative positioning method (differential method or an interference positioning method) which uses the following technique has started attracting the attention. In this method, the observation error component generated by the single positioning method is canceled by using information sent from a reference station installed at a known point and observation information at a mobile station thereby improving the positioning accuracy.
The GPS is a positioning system constituted by 24 GPS satellites which fly in a circular orbit having a height of about 20,000 km. The GPS began to be developed by the Department of Defense in United States of America in 1970s to be used by the military and other alliance. This GPS is a system which can singularly perform positioning at a high accuracy on the sea and the land, i.e., in any area on the earth, and has replaced the conventional hyperbolic navigation methods such as the omega navigation method, the Loran C navigation method, and the Decca navigation method. A part of the signals from the GPS satellites have been made open to the public under certain conditions. Some signals from this part are used as positioning information in the car navigation or the like.
At present, the methods which use the GPS to perform positioning are roughly classified into two methods and both of them use GPS positioning apparatuses:
(1) Single positioning method PA1 (2) Relative positioning method
The single positioning method mentioned above is the most basic positioning method. In this positioning method, at least four GPS satellites are simultaneously observed by a GPS positioning apparatus at an unknown point. On the basis of these four observation results, a total of four unknowns (latitude, longitude, height and clock error), i.e., unknown three-dimensional coordinates (latitude, longitude and height) and a clock error in the GPS positioning apparatus are obtained. More specifically, the GPS positioning apparatus calculates correlations between received signals (C/A codes) from the GPS satellites while the GPS positioning apparatus sequentially generates C/A codes (Clear and Acquisition) codes allocated to the GPS satellites to calculate propagation delay times. The C/A code is open to the public, and is a pseudo noise code having a code length of 1023 bits.
The GPS positioning apparatus then calculates pseudo distance up to the respective GPS satellite by multiplying the propagation delay times by the velocity of light. The pseudo distance is the sum of a true distance and an error distance between the GPS positioning apparatus and the satellite. Clock error, error of orbit information of the GPS satellite, fluctuation generated by the SA to the C/A code, propagation delay caused by the ionized layer, and propagation delay caused by the troposphere are generally the factors that generate an error in the measurement of the distance.
The GPS positioning apparatus obtains position information of each satellite from Ephemeris (satellite orbit information) included in a satellite message from each GPS satellite, and solves quaternary simultaneous equations (positioning equations) on the basis of the position information and the pseudo distance described above, thereby calculating the coordinates (X.sub.u, Y.sub.u, Z.sub.u) of an unknown point and a clock error (C.sub.BU). The quaternary simultaneous equations are expressed by the following equation (1): EQU (X.sub.i -X.sub.u).sup.2 +(Y.sub.i -Y.sub.u).sup.2 +(Z.sub.i -Z.sub.u).sup.2 =(R.sub.i -C.sub.BU).sup.2 (1)
wherein i (i=1, 2, 3, 4) represents a GPS satellite used in positioning, X.sub.i, Y.sub.i and Z.sub.i are coordinates (known) of the GPS satellite, X.sub.u, Y.sub.u and Z.sub.u are the positioning coordinates (unknown) of the GPS positioning apparatus, R.sub.i is the pseudo distance between the GPS positioning apparatus and the GPS satellite (known), and C.sub.BU is the clock error.
In this manner, in the single positioning method, the coordinates (X.sub.u, Y.sub.u, Z.sub.u) of an unknown point are calculated as positioning results. However, the positioning results include an error of orbit information of the GPS satellite described above, the error caused by a fluctuation generated intentionally by the SA to the C/A code, delay error caused by the ionized layer, and the error component based on a delay caused by the troposphere. Therefore, the positioning accuracy of the single positioning method is limited to about 100 m.
The relative positioning method of the item (2) is a method which performs positioning by using a plurality of GPS positioning apparatuses (a GPS positioning apparatus at a known point and a GPS positioning apparatus at an unknown point), and can perform positioning at an accuracy higher than that of the single positioning method of the item (1). The relative positioning methods are roughly classified into a differential method and an interference positioning method. The differential method is also called a DGPS (Differential GPS). According to the differential method, the GPS positioning apparatus at the known point and the GPS positioning apparatus at the unknown point perform single positioning using a pseudo distance to cancel a common error, thereby improving a positioning accuracy to several meters.
On the other hand, according to the interference positioning method, after the GPS positioning apparatus at the known point and the GPS positioning apparatus at the unknown point measure the phases (to be referred to as carrier wave phases hereinafter) of carrier waves from the GPS satellites, a base vector between the known point and the unknown point is calculated. Using this base vector, the relative three-dimensional coordinates of the known point with respect to the known point are calculated. Since this interference positioning method uses a carrier wave having a wavelength of about 20 cm, a resolution higher than that of the differential method using a C/A code having a wavelength of about 300 m is obtained. Thus, there is the advantage that the positioning accuracy is considerably improved.
A rough configuration of a GPS positioning system which uses the differential method and the interference positioning method will be described below with reference to FIG. 7. The GPS satellites 1A, 1B, 1C and 1D shown in FIG. 7 are the four GPS satellites out of the 24 GPS satellites, and are visible satellites which can be simultaneously observed from both of a known point and an unknown point. The known point is a known fixed point expressed by correct three-dimensional coordinates (latitude, longitude and height). On the other hand, the unknown point is a point whose position is to be obtained. This unknown point corresponds to the three-dimensional coordinates of a moving object (e.g. a car) 4 which changes it position at every moment.
The GPS satellites 1A, 1B, 1C and 1D always transmit signals required for positioning with carrier waves. In the GPS, two types of carrier waves for positioning are used, and the carrier waves are called L1 band (1575.42 MHz) and L2 band (1227.6 MHz), respectively. Two types of signals for positioning on the carrier waves of the L1 band and the L2 band are used, and the signals are called C/A code and P code, respectively. The C/A code is a code for positioning opening to the public, and has a code length of 1023 bits.
On the other hand, the P code is a code which is concealed for military use, and has a code length of about 6.times.10.sup.12 bits. The C/A code and the P code are called pseudo noise codes (PN code (Pseudo random Noise code)), and are digital codes each of which is constituted by irregularly ordering 0 and 1 at a glance. As array patterns of the PN codes, different array patterns are allocated to the 24 GPS satellites. The GPS satellites are identified by the different array patterns.
A C/A code and a satellite message are on the carrier wave of the L1 band, and only P code is on the carrier wave of the L2 band. The satellite message consists of a data group including satellite orbit information or the like required for a positioning calculation, and is digital data having a bit rate lower than those of the C/A code and the P code. More specifically, the satellite message includes satellite orbit information, coarse orbit information of all the GPS satellites, an ionized layer correction coefficient, a correction coefficient of a satellite clock (atomic clock) and the like.
A known point side GPS positioning apparatus 2 is installed at the known point, and receives radio waves from the GPS satellites 1A, 1B, 1C and 1D through a not shown GPS antenna to calculate a GPS observation amount. The known point side GPS positioning apparatus 2 is installed in a not shown reference station installed at the known point. In this case, when the differential method is used, the GPS observation amount is the pseudo distances from the known point side GPS positioning apparatus 2 up to the GPS satellites 1A, lB, 1C and 1D.
In the differential method, the known point side GPS positioning apparatus 2 applies the three-dimensional coordinates of the GPS satellites 1A, 1B, 1C and 1D obtained by the satellite massage and the three-dimensional coordinates of the known point to the Pythagoras theorem to calculate a geometrical distance (theoretical value). Further, the known point side GPS positioning apparatus 2 calculates a difference between the geometrical distance and the pseudo distance as a correction amount, and calculates a change rate of the correction amount with time. The correction amount and the change rate thereof are calculated with respect to the GPS satellites 1A, 1B, 1C and 1D.
The correction amount is an amount corresponding to an error of orbit information of an error component (an error of orbit information of a GPS satellite, part of an error caused by fluctuation given to a code by the SA, a propagation delay error caused by the ionized layer, and a propagation delay error caused by the troposphere) of positioning results obtained by the single positioning method. The known point side GPS positioning apparatus 2 transmits the correction amounts (differences) corresponding to the GPS satellites 1A, 1B, 1C and 1D and change rates of the correction amounts to a relaying station 3 (to be described later) as DGPS data.
On the other hand, in the interference positioning method, GPS observation amounts are carrier wave phases corresponding to the GPS satellites 1A, 1B, 1C and 1D in the known point side GPS positioning apparatus 2. In this case, the known point side GPS positioning apparatus 2 transmits the carrier wave phases and the three-dimensional coordinates of the known point to the relaying station 3 as interference positioning data.
The relaying station 3 is a station which transmits relays data (DGPS data or interference positioning data) to an unknown point side GPS positioning apparatus 5 mounted on the moving object 4. The relaying station 3 and the known point side GPS positioning apparatus 2 are connected to each other through a cable circuit (or radio circuit), and the relaying station 3 and the unknown point side GPS positioning apparatus 5 are connected to each other through a radio circuit.
Here, as the relaying station 3, for example, an FM (Frequency Modulation) broadcast station is used. In this case, data (DGPS data or interference positioning data) from the known point side GPS positioning apparatus 2 is got on an FM broadcast radio wave, and is broadcasted through an antenna 3a. As the antenna 3a, in addition to the FM broadcast station, a radio station for only the GPS, a medium wave beacon, a communication satellite, a navigation satellite or the like is used.
The moving object 4 has the unknown point side GPS positioning apparatus 5 mounted thereon. While the moving object 4 moves, the position (three dimensional coordinates) of the moving object 4 changes every moment. The unknown point side GPS positioning apparatus 5, like the known point side GPS positioning apparatus 2, receives radio waves from the GPS satellites 1A, 1B, 1C and 1D through a GPS antenna (not shown), respectively, so as to calculate GPS observation amounts.
More specifically, in the differential method, the unknown point side GPS positioning apparatus 5 calculates pseudo distances between the unknown point side GPS positioning apparatus 5 and the GPS satellites 1A, 1B, 1C and 1D. The unknown point side GPS positioning apparatus 5 subtracts a correction amount obtained by the DGPS data from the respective pseudo distances. With this subtraction, common error components (an error of orbit information of a GPS satellite, part of an error caused by fluctuation given to a code by the SA, a propagation delay error caused by the ionized layer, and a propagation delay error caused by the troposphere) of error components at the known point and the unknown point is canceled.
Next, the unknown point side GPS positioning apparatus 5 obtains position information of the satellites from Ephemeris (satellite orbit information) included in a satellite message from the GPS satellites 1A, 1B, 1C and 1D. The unknown point side GPS positioning apparatus 5, as in the single positioning method described above, solves quaternary simultaneous equations (positioning equations) on the basis of the position information and the subtraction results described above (distances from which the common errors are removed), thereby calculating the position (three-dimensional coordinates) of the unknown point. The details of the positioning method in this differential method will be described later with reference to FIG. 8.
On the other hand, in the interference positioning method, the unknown point side GPS positioning apparatus 5 calculates a path difference between radio waves from the same GPS satellite to the known point side GPS positioning apparatus 2 and the unknown point side GPS positioning apparatus 5 on the basis of the carrier wave phases corresponding to the GPS satellites 1A, 1B, 1C and 1D and the data (interference positioning data) from the relaying station 3. In fact, the path differences are calculated for the GPS satellites 1A, 1B, 1C and 1D, respectively.
The unknown point side GPS positioning apparatus 5 calculates a base vector from the known point to the unknown point on the basis of these path differences to obtain the position (three-dimensional coordinates) of the unknown point with respect to the known point. The details of the positioning method in the interference positioning method will be described below with reference to FIG. 9. In this manner, in the conventional differential method and the conventional interference positioning method, the relaying station 3 for relaying the data from the known point side GPS positioning apparatus 2 to the unknown point side GPS positioning apparatus 5 is necessary.
The positioning method in the differential method and the interference positioning method will be described below with reference to FIG. 8 and FIG. 9. The same reference numerals as in FIG. 7 denote the same parts in FIG. 8 and FIG. 9. First, the positioning method in the differential method will be described below with reference to FIG. 8.
In FIG. 8, the known point side GPS positioning apparatus 2 installed at the known point, as in the single positioning method described above, receives radio waves from the GPS satellites 1A, 1B, 1C and 1D through a not shown GPS antenna to calculate pseudo distances O.sub.1, O.sub.2, O.sub.3 and O.sub.4. These pseudo distances O.sub.1, O.sub.2, O.sub.3 and O.sub.4 include the clock error described above, error of orbit information of a GPS satellite, part of the error caused by fluctuation given to a code by the SA, propagation delay error caused by the ionized layer, and propagation delay error caused by the troposphere, respectively.
Next, the known point side GPS positioning apparatus 2 calculates geometrical distances as theoretical values C.sub.1, C.sub.2, C.sub.3 and C.sub.4 from the three-dimensional coordinates of the GPS satellites 1A, 1B, 1C and 1D and the three-dimensional coordinates of the known point. In addition, the known point side GPS positioning apparatus 2 calculates differences between the calculated pseudo distances O.sub.1, O.sub.2, O.sub.3 and O.sub.4 and the theoretical values C.sub.1, C.sub.2, C.sub.3 and C.sub.4 as correction amounts ((O.sub.1 -C.sub.1), (O.sub.2 -C.sub.2), (O.sub.3 -C.sub.3) and (O.sub.4 -C.sub.4)), respectively.
The correction amounts described above correspond to the error of orbit information of the GPS satellite, part of an error caused by fluctuation given to a code by the SA, a propagation delay error caused by the ionized layer, and a propagation delay error caused by the troposphere, respectively, and are common error components with respect to the unknown point side GPS positioning apparatus 5. In addition, the known point side GPS positioning apparatus 2 calculates change rates of the correction amounts ((O.sub.1 -C.sub.1), (O.sub.2 -C.sub.2), (O.sub.3 -C.sub.3) and (O.sub.4 -C.sub.4)) with time.
The known point side GPS positioning apparatus 2 transmits the correction amounts ((O.sub.1 -C.sub.1), (O.sub.2 -C.sub.2), (O.sub.3 -C.sub.3) and (O.sub.4 -C.sub.4)) and the change rates of the correction amounts to the relaying station 3. In this manner, DGPS data is transmitted through the antenna 3a of the relaying station 3. The DGPS data is received by the unknown point side GPS positioning apparatus 5.
In parallel to a receiving operation of a radio wave by the known point side GPS positioning apparatus 2, the unknown point side GPS positioning apparatus 5 receives radio waves from the GPS satellites 1A, 1B, 1C and 1D through the GPS antenna (not shown), thereby calculating pseudo distances O.sub.a, O.sub.b, O.sub.c and O.sub.d. The pseudo distances O.sub.a, O.sub.b, O.sub.c and O.sub.d include the common error components described above.
The unknown point side GPS positioning apparatus 5 obtains the correction amounts ((O.sub.1 -C.sub.1), (O.sub.2 -C.sub.2), (O.sub.3 -C.sub.3) and (O.sub.4 -C.sub.4)) and the change rates thereof from the received DGPS data. In addition, the unknown point side GPS positioning apparatus 5 uses the change rates to extrapolate correction amounts ((O.sub.1 -C.sub.1), (O.sub.2 -C.sub.2), (O.sub.3 -C.sub.3) and (O.sub.4 -C.sub.4)) at reception time of the radio waves from the GPS satellites 1A, 1B, 1C and 1D by extrapolation.
The unknown point side GPS positioning apparatus 5 subtracts the extrapolated correction amounts from the pseudo distances O.sub.a, O.sub.b, O.sub.c and O.sub.d, respectively. The subtraction results are the distances from which the common error components have been removed. In addition, the unknown point side GPS positioning apparatus 5 solves quaternary simultaneous equations (positioning equations) on the basis of the position information of the GPS satellites 1A, 1B, 1C and 1D and the subtraction results described above (distances from which common errors are removed) to calculate the position (three-dimensional coordinates) of the unknown point.
In this manner, on the basis of the DGPS data from the known point side GPS positioning apparatus 2, the common error components included in the pseudo distances O.sub.a, O.sub.b, O.sub.c and O.sub.d in the unknown point side GPS positioning apparatus 5 are removed. For this reason, the positioning results obtained by the differential method has an accuracy higher than that in the single positioning method.
The positioning method performed by the interference positioning method will be described below with reference to FIG. 9. The interference positioning method shown in FIG. 9 is a method called a real time kinematics method in which positioning results are obtained on real time by using data (interference positioning data) from the relaying station 3. A principles of the real time kinematics method will be described below.
In this real time kinematics method, principally, a difference (path difference PD) between a distance .rho..sub.a from the known point side GPS positioning apparatus 2 to the GPS satellite 1A and a distance .rho..sub.b from the unknown point side GPS positioning apparatus 5 to the same GPS satellite 1A is calculated. Similarly, path differences corresponding to the GPS positioning systems 1B, 1C, and 1D are calculated. In this case, the distances .rho..sub.a and .rho..sub.b and the path differences are calculated on the basis of the phases (carrier wave phases) of the carrier waves from the GPS satellites 1A, 1B, 1C and 1D. On the basis of the four path differences, a base vector D from the known point to the unknown point, in other words, the relative position of the unknown point with respect to the known point is calculated.
More specifically, the three-dimensional coordinates of the known point side GPS positioning apparatus 2 (known point) and the three-dimensional coordinates of the unknown point side GPS positioning apparatus 5 (unknown point) are represented by (X.sub.a, Y.sub.a, Z.sub.a) and (X.sub.b, Y.sub.b, Z.sub.b), and the three-dimensional coordinates of the ith GPS satellite at a moment (GPS satellite 1A in FIG. 9) are represented by (X.sub.i, Y.sub.i, Z.sub.i). The three-dimensional coordinates (X.sub.a, Y.sub.a, Z.sub.a) and (X.sub.i, Y.sub.i, Z.sub.i) are known, and (X.sub.b, Y.sub.b, Z.sub.b) are unknown numbers.
Under these conditions, the distance .rho..sub.a between the ith GPS satellite (GPS satellite 1A in FIG. 9) and known point side GPS positioning apparatus 2 is expressed by the next equation (2) according to the Pythagoras theorem: EQU .rho..sub.a ={(X.sub.i -X.sub.a).sup.2 +(Y.sub.i -Y.sub.a).sup.2 +(Z.sub.i -Z.sub.a).sup.2 }.sup.1/2 (2)
Similarly, the distance .rho..sub.b between the ith GPS satellite (GPS satellite 1A) and the unknown point side GPS positioning apparatus 5 is expressed by the following equation (3): EQU .rho..sub.a ={(X.sub.i -X.sub.b).sup.2 +(Y.sub.i -Y.sub.b).sup.2 +(Z.sub.i -Z.sub.b).sup.2 }.sup.1/2 (3)
Therefore, the path difference PD is expressed by the following equation (4) on the basis of the equations (2) and (3): EQU PD=.rho..sub.a -.rho..sub.b ={(X.sub.i -X.sub.a).sup.2 +(Y.sub.i -Y.sub.a).sup.2 +(Z.sub.i -Z.sub.a).sup.2 }.sup.1/2 -{(X.sub.i -X.sub.b).sup.2 +(Y.sub.i -Y.sub.b).sup.2 +(Z.sub.i -Z.sub.b).sup.2 }.sup.1/2 (4)
The path differences with respect to the remaining GPS positioning systems 1B and 1C are calculated as in the equation (4). As a result, ternary simultaneous equations are derived. The solutions (X.sub.b, Y.sub.b, Z.sub.b) of the ternary simultaneous equations are calculated by using a mathematical method such as linear combination or the method of least squares. The unknown numbers can be mathematically derived on the basis of the three GPS satellites. In fact, however, in order to remove clock error components in the GPS satellites, the known point side GPS positioning apparatus 2 and the unknown point side GPS positioning apparatus 5, derivation of the unknown numbers are performed on the basis of four GPS satellites.
The above is the mathematical positioning principle. In fact, the known point side GPS positioning apparatus 2 receives radio waves from the GPS satellites 1A, 1B, 1C and 1D to observe carrier wave phases K.sub.1, K.sub.2, K.sub.3 and K.sub.4. In this case, in the carrier wave phases K.sub.1, K.sub.2, K.sub.3 and K.sub.4, only decimal portions of wave numbers can be understood because the observation results of the known point side GPS positioning apparatus 2 are instantaneous phase values. More specifically, a wave number is expressed by the sum of an integer portion (one wavelength of carrier wave x integer) and the decimal portion. In the observation results, the integer portion is not fixed. This phenomenon is called phase ambiguity or integer bias.
The carrier wave phases K.sub.1, K.sub.2, K.sub.3 and K.sub.4 include error components consisting of phase ambiguity, a delay error caused by the ionized layer, a propagation delay error caused by the troposphere, a clock error and the like. The known point side GPS positioning apparatus 2 relays the carrier wave phases K.sub.1, K.sub.2, K.sub.3 andK.sub.4 serving as observation amounts and phase information (three-dimensional coordinates) of the known point to the relaying station 3 as interference positioning data. The interference positioning data is broadcasted by the relaying station 3.
On the other hand, the unknown point side GPS positioning apparatus 5, like the known point side GPS positioning apparatus 2, receives radio waves from the GPS satellites 1A, 1B, 1C and 1D to observe carrier wave phases K.sub.a, K.sub.b, K.sub.c and K.sub.d. In this case, the carrier wave phases K.sub.a, K.sub.b, K.sub.c and K.sub.d include error components consisting of phase ambiguity, a propagation delay error caused by the ionized layer, a propagation delay error caused by the troposphere, a clock error and the like.
The unknown point side GPS positioning apparatus 5 receives the interference positioning data from the relaying station 3 to linearly combine the carrier wave phases K.sub.1, K.sub.2, K.sub.3 and K.sub.4 and the carrier wave phases K.sub.a, K.sub.b, K.sub.c and K.sub.d, respectively, as expressed in the following equations (5) to (7), thereby calculating observation values K.sub.12ab, K.sub.13ac and K.sub.14ad on a mathematical model. EQU K.sub.12ab =(K.sub.1 -K.sub.a)-(K.sub.2 -K.sub.b) (5) EQU K.sub.13ac =(K.sub.1 -K.sub.a)-(K.sub.3 -K.sub.c) (6) EQU K.sub.14ac =(K.sub.1 -K.sub.a)-(K.sub.4 -K.sub.d) (7)
When the linear combination is performed as described above, common errors (delay errors or the like caused by the ionized layer) of the known point side GPS positioning apparatus 2 and the unknown point side GPS positioning apparatus 5 are canceled. The unknown point side GPS positioning apparatus 5 arithmetically operates the equations (5) to (7) by using the known method of least squares or a Kalman filter to fix the integer portions of the carrier wave phases, and calculates a base vector (X.sub.b, Y.sub.b, Z.sub.b) from the known point side GPS positioning apparatus 2 (the known point (X.sub.a, Y.sub.a, Z.sub.a) as positioning results. The positioning results are very high accurate because the positioning results are based on the phase of a carrier wave having a wavelength of about 20 cm.
Once the integer portion of the carrier wave phase is fixed, the integer portion need not be calculated unless the integer portion does not change. In order to make it rapid to perform arithmetic operation for fixing the integer portion of the carrier wave phase, it is desired that the number of visible GPS satellites which can be simultaneously seen from the known point side GPS positioning apparatus 2 and the unknown point side GPS positioning apparatus 5 is as large as possible.
In the differential method and the interference positioning method using a plurality of GPS positioning apparatuses, as has been described with reference to FIG. 8 and FIG. 9, at least four visible GPS satellites which can be simultaneously seen from the known point side GPS positioning apparatus 2 and the unknown point side GPS positioning apparatus 5 are required, and it is desired that the distance between the known point side GPS positioning apparatus 2 and the unknown point side GPS positioning apparatus 5 is as short as possible (10 km or less) to keep a high accuracy.
However, in order to satisfy the above condition in a wide area, as in a configuration constituted by a plurality of zones in a mobile telephone network, a large number of known point side GPS positioning apparatuses 2 (reference stations) and a large number of relaying stations 3 have to be installed at intervals of several 10 km. For this reason, installation costs are high. At present, service areas in which the known point side GPS positioning apparatuses 2 (reference stations) are installed are limited to bigger cities and the like, and the service areas do not reach mountainous regions and non-populated regions. Therefore, since positioning cannot be performed by a method other than the single positioning method in an area except for the service area, accurate positioning results cannot be obtained.
In addition, in the prior art, four or more visible GPS satellites which can be simultaneously seen from the known point side GPS positioning apparatus 2 and the unknown point side GPS positioning apparatus 5 are required. However, in particular, since a receiving location of a radio wave in the unknown point side GPS positioning apparatus 5 mounted on the moving object 4 frequently changes, only three or less visible GPS satellites may be simultaneously seen from the known point side GPS positioning apparatus 2 and the unknown point side GPS positioning apparatus 5. In this case, accurate positioning results cannot be obtained. When a radio circuit between the relaying station 3 and the unknown point side GPS positioning apparatus 5 is disconnected due to the influence of fading or the like, accurate positioning results cannot be obtained.
Furthermore, in the unknown point side GPS positioning apparatus 5, in addition to a receiving unit (antenna and receiving section) for receiving a radio wave from the GPS satellite 1A or the like, other receiving unit (antenna and receiving section) for receiving data from the relaying station 3 are required. The apparatus is increased in size by, especially, the antenna.